Did they push on with the allies, or stay back in France.
Yes, the French did take part in the Allied attack on Germany.
The French 1st Army was assigned to the extreme right (southern) flank of the Allied line, near the border of Switzerland. Following its successful defence (alongside the US 7th Army) in Operation Nordwind - the last German offensive in the West - in January 1945, the 1st Army crossed the Siegfried Line and Rhine, entering Germany on 31 March. They then went on to clear the southwestern corner of Germany, capturing Stuttgart.